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In the beginning, there was curiosity...

and from it grew... mathematics
and curiosity said: It is good.

Warning: Before reading this article, you should be informed of the following quote:

Joe, whenever somebody asks you the time, you build them a clock.
- C.E. Christensen
But, then I figure, if they had a clock, they wouldn't need to ask anyone else for the time, they would have the knowledge at their fingertips.

Aside comments and extensions of definitions

Oscillation of a field: Trying to define a particle in field theory is similar to trying to isolate an ocean wave from the ocean. While it is possible to distinguish (view) the oscillation, when you actually try to isolate the wave from the ocean, it is no longer a wave, but merely a pool of water. Just as a wave is defined as part of the ocean, a particle in field theory is merely a oscillation of a field.

There are two different types of field theory: Abelian and non-Abelian. See the aside regarding how these are different.

Abel, Abelian, and non-Abelian: The name Abelian comes from the mathematician Abel. (More about this at some future date.)

Technically, this refers to whether or not the elements of an algebra commute. Colloquially, can I rearrange the numbers which are being multiplied or added? That is, regular multiplication is Abelian (it commutes): 3x4 = 4x3 = 12. Regular addition is also Abelian (it commutes): 3+4 = 4+3 = 7. Matrices, however, do not commute under multiplication: Matrix multiplication is non-Abelian (it does not commute): AxB does not equal BxA, if A and B are matrices.

So what? Well, it turns out that if you can describe particles with Abelian multiplication, it is because those particles do not interact with each other. Photons (particles of light) are an example of this. Photons only interact with electrically charged particles, not with other photons.

On the other hand, if you need non-Abelian mathematics to describe the particles, then they can interact with themselves. This makes the interactions very much more complicated. This is the case for gluons, the particles which mediate the strong nuclear force (the interaction between quarks called quantum chromodynamics or QCD). Gluons do interact with other gluons as well as with particles which have a color charge (those which feel the strong nuclear force).

momentum vs energy: The energy is typically a bit more intuitive - actually, the kinetic energy is typically a bit more intuitive. In the context of this aside, I will be concerned with kinetic energy, as opposed to other types of energy. Objects which are moving quickly can be thought of as energetic. That is to say, they have more kinetic energy than a similar object with less speed. So, we can say that the kinetic energy depends on the speed of an object. In addition, we can see that it takes more energy to more heavier objects, thus we say that the kinetic energy also depends on the mass of the object that we are considering.

The momentum also depends on the mass, but it depends on the velocity (which is similar to and related to, but different from the speed). Because the momentum depends on the velocity, it inherently depends on the direction of motion. That is to say, the momentum is a vector. The kinetic energy, on the other hand is not a vector (see scalar). When a person is discussing the kinetic energy, they can talk about the amount of kinetic energy, but when discussing the momentum, the "amount" (referred to as magnitude) and the direction are relevant. In some cases, the direction is obvious and implied rather than explicit, but nonetheless, it is relevant.

The point of making this distinction is that while the energy is related to how much work it takes to make something move a certain speed in a more intuitive way, it is the momentum which tells us how it is moving and how it will interact with other objects that it encounters. For example, a truck that hits a car head on will make the car react differently from a truck that hits a car from the side - the direction is important.

order of magnitude: The order of magnitude refers to the approximate size of some quantity in some appropriate units. (see scientific notation) For example: a soda can is about 13 centimeters (or 0.13 meters or 1.3e-1 meters) long. It is on the order of 10^(-1) meters. A person who is 2 meters tall is on the order of 10^(0) meters. The Earth has a radius of 6.37e6 meters and so is on the order of 10^(6) meters. An elephant may be 3 meters tall, but this is still on the order of 10^(0) meters. So, after reading the aside on scale, we can again say a pencil {10^(-1)} is small compared to a person or an elephant {10^(0)}, but a pencil {10^(-10)} and an elephant {10^(0)} are not much different compared to the Earth {10^(6)}. Note that an atom is an the order of 10^(-10) meters and a proton is on the order of 10^(-15) meters.
scale: The word scale refers to the approximate size of a quantity. For example: the size of a soda can is about 5 inches, or 13 centimeters. So, anything that is a bit less than a half foot is on the scale of a soda can. A pencil and a worm are on the same scale. A pencil and an elephant are not the same scale, unless you compare them to something which is on a very different scale, like the Earth. In other words, compared to a person, a pencil and a worm are about the same size. Compared to the Earth, a pencil and an elephant are also about the same size. This idea is relative in that it depends on to what the comparison is made. The idea of order of magnitude is less vague.
scattering:
light wave: It was noticed by Maxwell that an electric field which changes in magnitude creates a magnetic field and that a magnetic field which changes in magnitude creates an electric field. This allows a combination of the two fields, an electromagnetic field, to propogate (move) through space by oscillating between the two forms. It was eventually realized that light is this electromagnetic wave. As interest in this phenomenon grew, a physical model to describe it was proposed. It was suggested that electromagnetic waves were like sound waves and that they propagated through some previously unknown medium (as sound waves propagate through air) that was called the luminiferous ether. Another scientist, Michelson, assisted by Morley, performed a remarkably clever experiment that proved the non-existence of this ether. What then were these waves which behaved like waves but yet were not like waves?